– dx x Inx x²+1

Q: Evaluate the integral. sin dx Se √1-x² 2

A:

Q: Use the indicated substitution to evaluate the integral.

A: Given: ∫121dxx2x2+4

Q: Evaluate the definite integral. (1 – x)² dx

A:

Q: Use u-substitution to find the definite integral |4xe -3x+7 dx . Please clearly show all -k.

A: By u - substitutions

Q: Use the Change of Variables Formula to evaluate the definite integral.

A:

Q: Find the integral: x8 9-x dx =

A:

Q: Evaluate the definite integral.

A:

Q: Evaluate the definite integral |(3xe¯*)dx

A:

Q: Evaluate the definite integral. xe dx Jo

A: using substitution method

Q: x2 – x dx -1

A: To evaluate the definite integral -1 to 1.

Q: Evaluate the definite integral. (x² – 2)² dx

A: Given that a finite integral and we solve it by using general formulas of integration. Here i…

Q: Use u-substitution to evaluate the integral: x/(x+2)^3   dx

A:

Q: Evaluate the definite integral. x° dx 12

A: Use power rule of integration ∫xndx=xn+1n+1, n≠-1 to evaluate the integral ∫24x3dx. Here n=3. Then…

Q: Evaluate the definite integral: 4 dx 0 x2+16

A:

Q: Evaluate the integral. sin dx 2 1-x

A:

Q: Evaluate the integral. 3x/2 2|sin x| dx Jo

A: We have to evaluate given integral:

Q: Evaluate the definite integral. (x² + 3)³x dx

A: This is a definite integral

Q: Use a substitution of the form u = ax + b to evaluate thefollowing indefinite integrals.∫(x + 1)12…

A: Given: ∫12x+1dx for evaluating this integral we substitute u=x+1 now differentiate both side with…

Q: +oo So xe-dx = 1

A: Evaluate: ∫0∞xe-xdx Apply infinte integral property: ∫a∞fx dx=limx→∞∫axfx dx ∫a∞xe-xdx…

Q: Use trigonometric substitution to find or evaluate the integral                      ∫√(x2 − 9) / x…

A: Integration: ∫x2-9xdxsubstitute, x2-9=z              xx2-9dx=dz                   dx=x2-9xdz…

Q: Evaluate the definite integral. dx 1+x

A: Evaluate: ∫05x1+xdx

Q: T(-8sec Xtonx-9see?x)dx=)

A:

Q: Evaluate the definite integrals. a) (x³ + 6x)dx

A:

Q: 2r cos x dx

A:

Q: Evaluate the definite integral.

A: Now consider,

Q: Evaluate the definite integral. 피/2 x° sin x dx -T/2 1 + x6

A: The given function is x6 sinx1+x6 We have to integrate this function over the interval -π2, π2.

Q: Evaluate this definite integral using a Geometric Formula: J(8-2x dx

A:

Q: Зx2 + 4х + 1 dx ). *3

A:

Q: dx c1 16. 21 1)

A:

Q: Evaluate the integral. X - 4 dx Jo x2 - 5x + 6

A:

Q: Evaluate the definite integral. (x – 3)ª dx

A: Given: I=∫13(x-3)4dx For evaluating given integral have to use formula mentioned below…

Q: しx(x*+) dx

A: Integration

Q: Evaluate the definite integral. S2 f(x) dx, ƒ (x) =(5sec2 x+7/tan x)//tan a

A:

Q: Evaluate the definite integral.

A:

Q: Evaluate the definite integral. · V½ dx

A:

Q: Evaluate the definite integral. dx .2 X* + 19 0.

A: Given: The definite integral∫09xx2+19dx To find the value of the given integral. Use the…

Q: 8. dx x - 1 5 08.

A:

Q: Rewrite as the equivalent definite integral in terms of u, but do not evaluate. 12x -dx (3x2 + 1)?…

A:

Q: evaluate the definite integral.

A:

Q: Evaluate the definite integral. хVx — 2 dx

A: Use substitutions to integration

Q: Evaluate the definite integral. '16 9e V x dx

A: Topic- Definite integration

Q: Evaluate the definite integral. dx x(1+ In æ)

A: Explained below

Q: Evaluate the definite integral. dx 3x + 6 0.

A: This definite integral can be solved by using the Substitution method as explained in step 2.

Q: b Write the following expression as a single definite integral of the form f(x) dx. [²Rx) dx =…

A:

Q: Evaluate the definite integral. 3 (x² – 2)2 dx

A:

Q: "evaluate the definite integral"

A:

Q: Evaluate the definite integral. (x2 - 2)2 dx

A: To find the integration

Q: Find the integral m tan -x X .2 1+x?

A: To find the given Integral.

Q: Evaluate the definite integral. (a) S, (x³ – 6x² + e-*)dx (b) S G+ 2)dx

A: a) ∫02x3-6x2+e-xdx=x44-6x33+e-x-102 Formula: ∫xndx=xn+1n+1 and ∫emxdx=emxm=x44-2x3-1ex02…

Q: Use the Change of Variables Formula to evaluate the definite integral. 6 In x dp- 1

A:

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.